\(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{5}\right)...\times\left(1-\frac{1}{100}\right)\)
=\(\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}\times...\times\frac{99}{100}\)
=\(\frac{1\times2\times3\times4\times...\times99}{2\times3\times4\times5\times...\times100}\)
= \(\frac{1}{100}\)